In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function, and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.

翻译：本文研究协变量调整回归函数的非参数推断。该参数刻画了在调整其他协变量后，连续暴露与结果之间的平均关联。特别地，在特定因果条件下，该参数对应所有个体被分配到特定暴露水平时的平均结果，即因果剂量-反应曲线。我们提出了一种协变量调整回归函数的去偏局部线性估计量，并证明该估计量逐点收敛于均值为零的正态极限分布。利用这一结果，我们构建了函数值及其差值的渐近有效置信区间。此外，我们通过经验过程上确界分布的近似结果，构建了渐近有效的一致置信带。我们的方法无需欠平滑处理，允许使用数据自适应估计量来估计干扰函数，且所提估计量达到了二阶可微函数的最优收敛速度。通过数值模拟以及空气污染暴露对心血管死亡率影响的分析，我们展示了该估计量的实际性能。